10.3 Define and use probability Algebra 2

Probability The probability of an event is a number from 0 to 1 that indicates the likelihood the event will occur. Theoretical Probability

Theoretical Probability When all outcomes are equally likely, the theoretical probability that an event A will occur is: P(A) = # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑒𝑣𝑒𝑛𝑡 𝐴 𝑇𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 The theoretical probability of an event is often simply called the probability of the event.

You pick a card from a standard deck of playing cards. Find the Ex. 1 - Probability You pick a card from a standard deck of playing cards. Find the A) probability of picking an 8 B) picking a red king

Ex. 2 Use Permutations or Combinations A cereal company plans to put 5 new cereals on the market: a wheat cereal, a rice cereal, a corn cereal, an oat cereal, and a multigrain cereal. The order in which the cereals are introduced will be randomly selected. Each cereal will have a different price. A.) What is the probability that the cereals are introduced in order of their suggested retail price? B) What is the probability that the first cereal introduced will be the multigrain cereal?

Odds in Favor or Odds against an event When all outcomes are equally likely, the odds in favor of an event A and the odds against a n event A are defined as follows: Odds in favor of event A = # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐴 # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑁𝑂𝑇 𝑖𝑛 𝐴 Odds against event A = # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑁𝑂𝑇 𝑖𝑛 𝐴 # 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐴

B) the odds against rolling an odd number. Ex. 3 A standard six-sided die is rolled. Find a) the odds in favor of rolling a 6. B) the odds against rolling an odd number.

Geometric Probability = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑝𝑎𝑟𝑡 𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ Geometric Probability – ratio of 2 lengths, areas or volumes (with the smaller on top and larger on the bottom). Geometric Probability = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑝𝑎𝑟𝑡 𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ Geometric Probability = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑚𝑎𝑙𝑙𝑒𝑟 𝑟𝑒𝑔𝑖𝑜𝑛 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑙𝑎𝑟𝑔𝑒𝑟 𝑟𝑒𝑔𝑖𝑜𝑛 Geometric Probability = 𝑆𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑉𝑜𝑙𝑢𝑚𝑒 𝐿𝑎𝑟𝑔𝑒𝑠𝑡 𝑉𝑜𝑙𝑢𝑚𝑒

Geometric Probability – ratio of 2 lengths, areas or volumes (with the smaller on top and larger on the bottom). Ex. 4 The standard archery target used in competition has a diameter of 80 centimeters. Find the probability that an arrow shot at the target will hit the center circle, which has a diameter of 16 centimeters. Assume the arrow will hit the target and is equally likely to hit any point inside the target.